THE UNFOLDING OF THE SPECTRA OF LOW ENERGY
GALACTIC COSMIC RAY H AND HE NUCLEI AS THE
VOYAGER 1 SPACECRAFT EXITS THE REGION
OF HELIOSPHERIC MODULATION
W.R. Webber1, P.R. Higbie2 and F.B. McDonald3+
1. New Mexico State University, Department of Astronomy, Las Cruces, NM 88003, USA
2. New Mexico State University, Physics Department, Las Cruces, NM 88003, USA
3. University of Maryland, Institute of Physical Science and Technology, College Park, MD
20742, USA
+ Deceased August 31, 2012
2
ABSTRACT
This paper describes the unfolding of the solar modulated galactic cosmic ray H and He
nuclei spectra beyond ~105 AU in the heliosheath. Between 2008.0 and 2012.3 when Voyager 1
went from about 105 to 120.5 AU the spectral intensities of these two components between about
30 and 500 MeV/nuc unfolded (increased) in a manner consistent with an average modulation
potential decrease ~5 MV per AU as described by a Parker like cosmic ray transport in the
heliosphere where the overall modulation is described by a modulation potential in MV.
Between 120.5 and 121.7 AU, however, as a result of two sudden intensity increases starting on
May 8th and August 25th, 2012, this modulation potential decreased by ~80 MV and spectra
resembling possible local interstellar spectra for H and He were revealed. Considering these
spectra to be the local interstellar spectra would imply that almost 1/3 of the total modulation
potential of about 270 MV required to explain the spectra of these components observed at the
Earth must occur in just a 1 AU radial interval in the outer heliosheath. As a result about ~80%
of the total modulation potential observed at the Earth at this time occurs in the heliosheath itself.
The remaining 20% of the total modulation occurs inside the heliospheric termination shock.
The details of these intensity changes and their description by a simple modulation model are
discussed.
3
Introduction
In late 2004 Voyager 1 crossed the heliospheric termination shock (HTS) at a distance of
94 AU from the Sun at a latitude of 34�N (Stone, et al., 2005). In analogy to what was observed
at V2 when it crossed the HTS later in 2007, the radial solar wind speed at V1 most likely
decreased from an average ~400 km�s-1 to ~130 km�s-1 (Richardson, et al., 2008) and then later to
a value close to zero (Krimigis, et al., 2011), and the magnetic field became larger and more
turbulent (Burlaga, et al., 2005). The cosmic ray diffusion coefficient in this field therefore
became much smaller after the shock crossing.
As a result of these parameter changes, the process by which galactic cosmic rays (GCR)
move inward in the heliosphere in this region beyond the HTS could be quite different than the
usual Parker process (1958) which describes cosmic ray modulation inside the HTS. however it
may still be characterized as a modulation potential. The Parker process assumes an expanding
solar wind with a Betatron like deceleration process, which can be described as a potential
difference, along with convection and diffusion.
The intensities of GCR nuclei and electrons are indeed observed to increase substantially
beyond the HTS (e.g., McDonald, et al., 2006, 2012). For electrons from ~6-100 MeV this
increase, up to 2012.7 when V1 is at 121.7 AU, is a factor of at least 100 in the heliosheath. This
increase occurs over a distance of ~27.7 AU between the HTS crossing distance and 121.7 AU.
This compares with a factor ~2 or less increase of these electrons between the Earth and the HTS
over a distance ~90 AU.
For cosmic ray nuclei the unfolding of the H and He nuclei spectra is more modest, but at
an energy of 145 MeV for protons the intensity increase beyond the HTS is nearly a factor ~10
and for He nuclei at this same energy, the factor is ~5. For these same particles between the
Earth and 72 AU, corresponding to the minima in the solar modulation in 1977 and 1998, the
radial increase observed by Voyagers 1 and 2 is a factor of about 3 for protons and ~2 for He
nuclei. Thus most of the solar modulation of these GCR components at these lower energies also
appears to be taking place in the region beyond the HTS.
In the 1st 3 years after the HTS crossing (about 11 AU in outward motion for V1) the
intensities of all components generally increased and the apparent radial intensity gradients,
especially for electrons, were relatively large and variable. These gradients then become more
regular beyond about 105 AU. At distances of 111 and 116 AU, sudden (< 1-26 day solar
4
rotation period) intensity changes and radial gradient changes are observed for electrons
(Webber, et al., 2012). These changes appear to be caused by the passage of V1 into different
regions (structures or sectors) at these locations which are at distances of ~17 and 22 AU beyond
the HTS crossing distance (e.g., Florinski, et al., 2011). Throughout this time period the energy
spectra of H and He nuclei have unfolded in a manner consistent with that to be expected in a
simple “Parker like” modulation model where the potential difference between the Voyager
location and that representing the cosmic ray source spectra is decreasing (Webber, 2012). On
average the potential difference associated with this modulation appears to decrease by about 2025 MV per year from 2008 to 2012 as Voyager goes from ~105 to 120 AU.
It is the object of this paper to chronicle this spectral unfolding for H and He nuclei,
extending the measurements to beyond 120 AU where the changes are even more dramatic than
those inside 120 AU, and to interpret all of these changes in the simplest available modulation
model, albeit that the conditions, particularly in the outer heliosheath being traversed by V1, are
most unusual.
A Description of the Data
In Figure 1 we show the radial intensity increases for H and He nuclei for various
energies between about 2006.6 and the end of 2012 when V1 is between 100 and 123 AU. The
data represents 6 month averages until 2011 when the time intervals become finer; eventually
decreasing to 26 day intervals in 2012. This is to show, in particular, the two significant
intensity increases of both nuclei and electrons in 2012. However, in the time from about 2007
to late 2011 the apparent radial intensity gradient is, on average, almost constant for each of the
individual energies/charges that are plotted. This average gradient for each curve in %/AU is
shown in the Figure.
These last two increases and their relative magnitude are shown in more temporal detail
in Figure 2 for nuclei >200 MeV. The total increase of the high energy nuclei is ~31% with 14%
of this increase occurring in the 1st step. A stepwise increase of this magnitude is unprecedented.
The data in Figures 3 and 4 is in the form of energy spectra for H and He nuclei obtained
from the HET telescopes on the Voyager CRS experiment (Stone, et al., 1977), see also Webber
and Higbie, 2009, for details on how the spectra are obtained. Also included in the figures are
curves calculated for a modulation model to be described later with parameters chosen to match
the data. The study of the spectral details for electrons and heavier nuclei in this time period will
5
be deferred to later papers but are also characteristic of a large sudden change in the modulation
potential. The figures 3 and 4 for the H and He nuclei are matched in intensity and energy scale
so that the figures can be simply over-laid to compare the relative intensity changes. The figures
show the intensities measured at the following times: 2008.0 (105.0 AU), 2010.0 (112.2 AU),
2012.0 (119.3 AU) and a period after 2012.7 (122.0 AU). The data at 2012.0 and after 2012.7
comes from the paper by Stone, et al., 2013. Each spectral point for 2008.0 and 2010.0 is a one
year average centered on the dates indicated so that short term changes are smoothed out. Also
shown in the two figures, in addition to the V1 spectra after 2008.0, are the H and He nuclei
spectra measured in 1998-99 when V1 was at 72 AU, still inside the HTS, but at a time when
intensities were at a maximum in the 11 year solar cycle (Webber, McDonald and Lukasiak,
2003).
For comparison to this Voyager data we show the spectra reported for H and He nuclei by
the PAMELA experiment near the Earth at the end of 2009 (Adriani, et al, 2013) at the time of
the highest intensity maximum for cosmic rays of modern times (McDonald, et al., 2010;
Mewaldt, et al., 2010).
The Voyager spectra presented here are background corrected when necessary. For
protons and He nuclei a correction is made for lower energy anomalous particles. At 100 MeV
this correction at 2012.0 and earlier times is ~50% of the total measured intensity for protons. At
this same energy this correction is ~15% for He nuclei. These low energy anomalous particle
spectra have exponents between ~-2.5 to -3.5 at ~100 MeV and above so that this correction
rapidly becomes less at higher energies. At lower energies this limits the energy to which the
GCR proton spectrum can be derived (taken to be ~50% background) at 2012.0 and earlier to
about 80 MeV. For He this minimum energy is ~60 MeV/nuc.
The proton spectra in Figure 3 therefore cover the energy range from 80-350 MeV and
the Helium spectra in Figure 4 from 60-630 MeV/nuc.
In Figure 3 for protons the total unfolding (increase) from 2008.0 to the time period after
the final increase starting at 2012.35 is a factor ~3.61 at 145 MeV; at 310 MeV this unfolding
factor is 2.16 and this factor is systematically decreasing with increasing energy. For He nuclei
in Figure 4 this total unfolding factor at 62 MeV/nuc is 5.18; at 145 MeV/nuc it is 2.73 and at
310 MeV/nuc this factor is = 1.55, again systematically decreasing with increasing energy but
now the fractional increase is much smaller than for protons at the same energy.
6
Although the intensities in 1998-99 at 72 AU inside the HTS measured by V1 are at an
intensity maximum in the 11 year solar modulation cycle they are still well below what was
observed for the same species later in 2008.0 at 105.0 AU in the heliosheath at a time when the
overall solar modulation potential was much greater. The intensity increase between 1998 at 72
AU and 2008.0 at 105 AU at V1 is a factor ~1.45 for protons at 145 MeV and ~1.28 for He at the
same energy/nuc. And since 2008.0 is a time when the solar modulation effects at the Earth
were actually greater than at 1998-99, the intensities at 105.0 AU in the heliosheath might have
been expected to be less than in 1998-99 at 72 AU due to the increased solar modulation at that
time. This underscores the rapid increase of intensities in the heliosheath.
Of special interest in this paper are the spectral changes taking place at 2012.35 and
2012.65. This is an overall time period when the radial distance to V1 changes by only 1.1 AU
from 120.6 to 121.7 AU. At ~145 MeV, the lowest energy for which the anomalous cosmic ray
(ACR) background can accurately be subtracted from the total proton spectrum at 2012.0, the
spectral unfolding factor is 1.90 for this short time period, which is about the same as the total
intensity increase for the 4 years between 2008.0 and 2012.35 when V1 moved outward 15.5
AU. At 310 MeV the unfolding factor for this same short time period is 1.50 for protons, again
about the same as the increase between 2008.0 and 2012.0.
For He nuclei at 62 MeV/nuc the unfolding factor for the time interval between 2012.35
and 2012.65 and between 2008.0 and 2012.0 are 2.28 and 2.25 respectively; at 145 MeV/nuc for
He they are 1.64 and 1.55 respectively; at 310 MeV/nuc they are 1.28 and 1.22 respectively.
Again these ratios are similar for both time periods covering ~1.1 AU and 15.5 AU respectively
of outward movement by Voyager, indicting a similar energy/rigidity dependence of the intensity
changes in both time periods.
To summarize, for H and He nuclei above about 60 MeV/nuc, the intensity changes
defining the overall modulation are similar in the two time periods, the 1 st time period covering
the ~1 AU thick region at 121 AU and the second time interval covering the outer 15.5 AU of the
heliosheath between 105-120.5 AU.
Comparison of Voyager Data with Data at the Earth
Here we compare here the Voyager intensities with the intensities for protons and Helium
nuclei that have been reported from the PAMELA experiment. This experiment has been
operating over the time period from 2006 to 2012 and therefore covers the time of intensity
7
maximum at the Earth in late 2009. The PAMELA data, (Adriani, et al., 2013) is also shown in
Figure 3 for protons and Figure 4 for He nuclei.
For both protons and Helium nuclei it is seen that the Voyager and PAMELA data sets
cover similar energy and time regimes. The intensities for both protons and He nuclei measured
by PAMELA at the time of the intensity maximum in solar cycle #24 in 2009 at the Earth are
comparable to but slightly less than those measured by Voyager 1 at a distance of 72 AU at the
time of maximum intensity in 1998 in solar cycle #23, 11 years earlier. This similarity of
intensities at 1 and 72 AU suggests; (1) There is a rather weak amount of overall modulation
throughout the inner heliosphere; (2) The uniqueness of the high intensities of these nuclei
observed at the Earth in 2009 (e.g., McDonald, et al., 2010; Mewaldt, et al., 2010).
These high intensities near the Earth at 2009 are characterized by the extremely low
modulation potentials ~250-270 MV that are required to reproduce the intensities and spectra of
H, He and heavier nuclei that are observed at this time (e.g., Wiedenbeck, et al., 2012).
Cosmic Ray Transport in the Heliosphere
Here we consider a spherically symmetric quasisteady state two radial zone (or hybrid)
no-drift transport model for cosmic rays in the heliosphere. This model has been previously used
by us on several occasions to describe the modulation of protons, Helium nuclei and Carbon
nuclei measured by V1 and V2 between ~2005 and 2011 when V1 and V2 were both inside and
outside the HTS at distances of between 70 and 115 AU from the Sun (Webber, et al., 2011a,
2011b and 2012). While this simplified model, which does not include drifts, obviously cannot
fit all types of observations it does provide a useful insight into the relative inner
heliospheric/outer heliospheric modulation and helps to determine which aspects of this
modulation need more sophisticated models for their explanation. The numerical model was
originally provided to us by Moraal (2003, private communication) and is similar to the model
described originally in Reinecke, Moraal and McDonald, 1993, and in Caballero-Lopez and
Moraal, 2004, and also similar to the spherically symmetric transport model described by Jokipii,
Kota and Merenyi, 1993 which does include drifts (Figure 3 of that paper). The basic transport
equation is (Gleeson and Urch, 1971);
8
Here f is the cosmic ray distribution function, p is momentum, V is the solar wind velocity,
K(r,p,t) is the diffusion tensor, Q is a source term and C is the so called Compton-Getting
coefficient. The final term on the left includes energy loss.
For spherical symmetry (and considering latitude effects to be unimportant for this
calculation) the diffusion tensor becomes a single radial coefficient Krr. We assume that this
coefficient is separable in the form Kr(r,P) = � K1(P) K2 (r), where the rigidity part, K1(P) � K1
and radial part, K2(r)�� K2. The rigidity dependence of K1(P) is assumed to be ~P above a low
rigidity limit PB. The units of the coefficient Krr are in terms of the solar wind speed V = 4 x
102.km.s-1 and the distance 1 AU=1.5 x 108 Km, so Krr = 6 x 1020 cm2.s-1 when K1 = 1.0.
Based on our earlier modulation studies at the Earth and V2 and V1 using protons,
Helium nuclei and Carbon nuclei (Webber, et al., 2011a, 2011b, 2012) we consider a distinct two
zone heliosphere (as was done by Jokipii, Kota and Merenyi, 1993). In this case the inner zone
extends out to 94 AU, the average distance to the HTS. In this inner region V=400 km.s-1 and
the diffusion parameters K1 and K2 are determined in our approach by a fit to the cosmic ray
data being compared.
The outer zone extends from the average HTS distance of about 94 AU to ~122 AU, the
approximate distance to the equivalent “outer modulation boundary”. This region is essentially
the heliosheath. In this region V is taken to be 130 km.s-1 (from V2 measurements, Richardson,
et al., 2008) and the diffusion parameters are K1H and K2H, which are greatly different from
those in the inner heliosphere are again determined by the fit to the cosmic ray intensity changes
observed at V1. The location of this outer boundary and the LIS spectra are important in this
calculation.
For the LIS H and He spectra we are fortunate that during the writing of this article, V1
appears to have exited the main solar modulating region as a result of the two sudden and large
increases at 2012.35 and 2012.65 mentioned earlier.
Also at 2012.65, as a result of the
disappearance of energetic ions ~1-80 MeV (ACR), V1 also appears to have exited the
confinement region for these low energy particles within the heliosheath. The intensity decrease
of these ACR is so large (over a factor ~100) and so rapid (a few days) that the entire and much
weaker GCR H and He low energy spectra are suddenly revealed, perhaps down to energies of a
few MeV. Furthermore, the higher energy GCR nuclei (~100-200 MeV and above) increased by
a factor of up to 1.5 in just a few days at the same time the ACR decreased.
9
Thus for the LIS spectra needed in this paper we will assume that the intensities
measured by Stone, et al., 2013, at V1 between about 2012.75 and 2013.0 for H and He nuclei
are indeed the LIS ones. These observed spectra can be approximated to an accuracy ~few %
above a few MeV by:
H FLIS = (20.2/T2.70)/(1+(6.75/T1.22)+(0.50/T2.80)+(0.0002/T4.42))
He FLIS = (0.94/T2.70)/(1+(4.14/T1.09)+(0.30/T2.79)+(0.00012/T4.26))
where T is in GeV/nuc.
To illustrate the diffusion coefficient that is used in the calculation in the two zones of
the heliosphere, we show Figure 5 which presents the values and rigidity dependence of this
parameter. At rigidities greater than ~300 MV, which includes most of the GCR nuclei, this
coefficient is taken to be ~P1.0 and has a value in the inner heliosphere, K1=200 at 1 GV
(=200x6x1020)= 1.2x1023 cm2�s-1. In the heliosheath the value of K1, K1H, is taken to be =12
(16.5 times smaller) at 1 GV.
The calculated modulated spectra corresponding to successive modulation potential
differences of 8 MV corresponding to the three 1 AU radial intervals between 119-122 AU are
shown in Figures 3 and 4 respectively for H and He nuclei. The radial spacing is then changed to
7 AU (119, 112 and 105 AU) corresponding to total modulation potentials of 24, 80 and 136 MV
with reference to the boundary taken to be 122 AU (in one year the V1 radial distance increases
by 3.6 AU). The modulated spectra are also shown at the HTS at 95 AU (about 220 MV) and at
the Earth (270 MV) for these same diffusion coefficients.
These calculated spectra give a good representation of the observed spectral unfolding at
V1 between 2008.0 to 2012.0 for total modulation potentials of between 136 and 80 MV
respectively for H and 160 and 110 MV respectively for He nuclei.
At 2012.0 the spectra of H and He would therefore require a further modulation potential
decrease ~80 and ~110 MV respectively for H and He nuclei at an energy ~145 MeV/nuc in
order to reach the FLIS representation of the LIS as observed by V1 later in 2012. This decrease
in potential would need to occur over a distance ~1 AU.
General Comments Regarding the Overall Modulation in the Heliosphere
The modulated spectra we have presented in Figures 3 and 4 represent a very simple
overall modulation picture at a single time and with radially independent diffusion coefficients in
the two radial zones of the heliosphere. Although there is general good agreement with the data
10
there are a number of specific differences between the predictions and observations that deserve
further comment. But before doing this, we should note the following. The total modulation
potential from the boundary at 122 AU to 1 AU is ~270 MV using these parameters. Using this
value, we are able to fit the measured intensities of H and He nuclei at the Earth in late 2009
measured by PAMELA (Adriani, et al., 2013) at a time when this modulation potential reached
its lowest values since accurate modern data have been available (McDonald, et al., 2010;
Mewaldt, et al., 2010). This value is consistent with the total modulation potential as obtained
from the Carbon spectrum measured by the CRIS-SIS experiment on ACE at this time which
was ~250 MV (Wiedenbeck, et al., 2012).
Of the 270 MV modulation potential that is calculated at the Earth at this time, ~80 MV
occurs in the two sudden steps near 121 AU. The total modulation in the rest of the heliosheath
is ~5 MV/AU x 28 AU, the thickness of the heliosheath, giving a total of ~220 MV in the entire
heliosheath. The remaining 50 MV occurs in the region from 1 AU out to the HTS at 95 AU.
However, this still produces a significant radial gradient in the inner heliosphere region
particularly at higher energies.
Note that these modulation potentials are for sunspot minimum conditions. Additional
modulation occurring during the normal solar 11 year modulation cycles which increases this
modulation potential is believed to occur mainly within the inner heliosphere, i.e., out to the HTS
at approximately 95 AU.
Similar modulation fractions for the outer and inner heliosphere are described by
Potgieter (2008).
Modulation at Sunspot Minimum in Opposite Solar Polarity Cycles – the 1998-99 V1 data
at 72 AU and Recent PAMELA Data in 2009
Once the LIS spectrum is actually available the overall heliospheric modulation potential
can be well determined by intensity measurements at the Earth. What is much less certain is the
relative fraction of the modulation potential that occurs inside the HTS to that between the HTS
and the modulation boundary. For example, in our model, at 2009 at the solar cycle minimum,
this relative fraction of inner to total heliospheric modulation is calculated to be 0.18 (50/270)
MV. In other words 18% of the modulation potential occurs inside the HTS.
In 1998-99 at the positive solar cycle #23 modulation minimum 11 years earlier, the
intensities of 145 MeV H nuclei measured at V1 at 72 AU are somewhat higher than those
11
measured by PAMELA at the Earth in 2009, but only by a factor ~1.30. In 1998, however, the
ratio of H nuclei intensities between 72 and 1 AU is ~2.0 at this energy. The ratio of the LIS
intensity to that at 1 AU at this time is ~10. So that from these measured intensity ratios at a
single time, roughly 20% of the total modulation is occurring between 1 and 72 AU, compatible
with our estimates above.
The Spectral and Intensity Changes of H and He Nuclei Starting on May 8 th and August
25th, 2012
It is evident from Figure 1 of this paper, which describes the time history of intensities
during the time period that V1 is passing through the outer heliosheath after about 2006.0, that
the grand finale of GCR increases in 2012 occurred in two steps. These steps are shown in
Figure 2. The 1st increase started on May 8, 2012, and took about 26 days to complete. It was
followed by a plateau of almost constant intensity for GCR nuclei and electrons which lasted
about 52 days. Then two sudden temporary increases in GCR of duration ~3 days and ~7 days,
respectively, occurred with the onsets of the increases separated by ~16 days. This was followed
by the final increase which started 13 days after the onset of the last of the two precursor
increases. This final GCR increase was basically completed in ~7 days for the nuclei considered
here and was the largest intensity increase of these GCR components since the launch of V1 35
years ago.
The most statistically accurate measure of the comparative increases during steps 1 and 2
comes from the PGH rate (H>200 MeV, e>12 MeV) shown in Figure 2. The increases in this
rate are 13.3�0.7% for the 1st increase and 33.4�1.4% for the total increase.
Regarding the rigidity/energy dependence of the overall two step increase of GCR H and
He nuclei, which is one of the most important aspects defining the mechanism of this episode of
modulation, we show in Figure 6 a plot of the calculated intensity changes, ln j2/j1 vs. P, for H
nuclei for a potential difference (E loss) of 80 MV in our model. This calculation is also shown
for He nuclei in the same figure. This figure illustrates a P-1.0 dependence of the modulation
above ~1 GV where the H and He input spectra are taken to be ~P-2.0. This dependence of ln j2/j1
vs. P is characteristic of our choice of the P1.0 rigidity dependence of the diffusion coefficient. A
turn up and splitting of the H and He intensity changes is calculated to occur at lower rigidities.
This splitting is due to differences in the LIS rigidity spectra of H and He at lower rigidities and
also to the different rigidities at which the intensity maximum occurs.
12
The actual observed intensity changes during this time period for H and He nuclei are
shown in Figure 6 alongside the predictions.
The agreement between predictions and
observations for H nuclei is excellent over the entire rigidity range. The agreement for He nuclei
is less good, however. A “splitting” between the magnitude of the H and He intensity changes is
indeed observed at a fixed rigidity, but this splitting appears to be larger than indicated by the
calculations.
From this comparison it appears that the final 2 step increase exhibited spectral intensity
changes that were consistent with an E loss mechanism.
Summary and Conclusions
The paper presents a summary of the unfolding of the energy spectra of H and He nuclei
in the heliosheath as measured on V1. This spectral unfolding occurs between about 105 and
122 AU as V1 approaches the outer boundary of the main heliospheric modulating region. The
observed spectral unfolding is well represented to first order by the spherically symmetric two
zone modulation model used here, a “Parker” based diffusion-convection model. Based on this
model the V1 data on H and He nuclei would suggest an energy loss potential difference that
decreases by 20-25 MV/year from a value ~180 MV to 80 MV between 2008 and 2012 when V1
is between 105-120 AU in the heliosheath.
Between 120.6 and 121.7 AU an additional
modulation potential decrease of 80 MV is necessary to explain the two sudden increases of the
intensity of lower energy H and He nuclei that occur in 2012. This potential difference in a 1
AU transition region amounts to ~1/3 of the total modulation potential of 270 MV between the
Earth and 121.7 AU at this time.
Although this unfolding of H and He nuclei spectra in the heliosheath can be reasonably
well fit using a Parker-like model with a potential energy loss, using the formulation that has
been originally applied to the inner heliosphere, most of the total heliospheric modulation at this
time is actually taking place well beyond the HTS which is located at about 94 AU. In the
heliosheath the value of the diffusion coefficient required to produce this modulation is only
about 1/15th of its average value inside the HTS.
This modulation even continues to take place in the region beyond ~112 AU where
Krimigis, et al., 2011, have determined that the average solar wind speed (the convective and E
loss terms in the Parker equation) approaches zero.
13
The large modulation taking place between 120.6 and 121.7 AU is difficult to understand
physically although its overall effect is described quite well by the simple models we use here.
For H nuclei the changes resemble those to be expected for a total potential loss ~80 MV taking
place in two almost equal steps. For He nuclei this potential loss is slightly larger. For this
energy loss to occur over ~1 AU in a Parker like modulation would require a diffusion
coefficient (literally a diffusion barrier) ~10 times smaller than the already small average
diffusion coefficient that we have used to describe the heliosheath spectral intensity unfolding
between 105 and 120 AU.
As a result of the final unfolding between 120.6 and 121.7 AU, a spectrum of lower
energy H and He nuclei is revealed down to perhaps 2 MeV. This spectrum is very similar to
that estimated from simple diffusion models of cosmic ray transport in the galaxy (e.g., Ip and
Axford, 1985; Putze, et al., 2011). Comparing the calculated spectra for Parker like modulation
levels which use modulation potentials of only a few MV with the actual measured H and He
spectra at these lower intensities restricts possible lower level modulation effect outside of the
normal heliosphere to probably less than ~10 MV of a Parker-like modulation potential (see,
however, Strauss, et al., 2013).
Other localized effects on the LIS spectra as described by Stone, et al., 2013, should be
observable from the intensity gradient as V1 proceeds further beyond this boundary. New
specific galactic propagation models extending down to a few MeV are needed to define the
expected LIS spectrum in this here-to-for unexplored region of the spectrum.
Acknowledgements
We appreciate the support of JPL for the Voyager program and from our colleagues Ed
Stone, Project Manager, and Alan Cummings on the West Coast and Nand Lal and Bryant
Heikkila on the East Coast. The H and He data used here comes from the Stone, et al., 2013,
Science paper and from internal web-sites maintained by Nand Lal and Bryant Heikkila.
14
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Webber, W.R., (2012), AIP Conf. Proc., 1516, 89-96
Webber, W.R. and P.R. Higbie (2009),J. Geophys. Res., 114, 2103
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Wiedenbeck, M.E., (2011), Space Sci. Rev., 176, 35-46
15
Figure Captions
Figure 1: Intensity changes of H and He nuclei for various energies between 2005 and 2012
when V1 is between ~100-123 AU in the heliosheath. The values of the average radial
gradient between 2005.0 and 2012.0 in %/AU are shown next to the intensity lines. The
data are 6 month averages up to 2012.0 and 26 day averages in 2012.
Figure 2: Five day running averages of the >200 MeV rate from 2011.8-2012.9 showing the
relative magnitude of the two increases starting on May 8 and August 25.
Figure 3: Yearly average H nuclei intensities centered at 2008.0, 2010.0 2012.0 and also the
time period from 2012.70 to 2013.0. The intensities measured at V1 in 1998-99 at the time
of the previous modulation minimum are also shown as well as the PAMELA intensities in
late 2009 at the Earth. Calculated spectra are shown for modulation levels in MV with
reference to the FLIS=LIS. The shaded band shows the amount of modulation occurring in
the inner heliosphere between the Earth and the HTS.
Figure 4: Same as Figure 2 but for He nuclei.
Figure 5: The values and rigidity dependence of the diffusion coefficients used in the inner and
outer heliospheric modulating regions. Note the sudden break of the rigidity dependence
from ~P1.0 to ~P-1.0, at 300 MV in the inner zone and at 150 MV in the outer zone. The
rigidity dependence and magnitude of the diffusion coefficients appropriate to lower rigidity
electrons that are shown as a shaded region in the Figure are quite different than those above
a few hundred MV that apply to the nuclei being modeled here.
Figure 6: TOP - The fractional intensity change, ℓn j2/j1, vs. P (MV) for H and He nuclei
calculated using our model parameters for a decrease in modulation potential from 80 MV to
zero (solid lines). The observed intensity changes at V1 from before May 8th to after August
25, 2012 are shown as open circles, black for H nuclei between 79 and 570 MeV and red for
He nuclei between 62 and 570 MeV/nuc. A fractional intensity change ~P-1.0 is also shown
for reference.
BOTTOM – Average radial intensity gradients in %/AU between 100 and 120 AU for H
(red) and He nuclei (black).
16
(P/cm2.s.sr.MeV/nuc)
4
2
4.40%
1
5.11%
0.894
0.6
Hex2
2.76%
182 He
1.33%
182 H/10
430 He
0.4
07.0
100
08.0
09.0
10.0
110
RADIUS (AU)
FIGURE 1
11.0 11.5 12.0 12.5 13.0 DATE
120
17
PGH RATE/sec x 2
4.8
4.4
4
3.6
PGH
2012
2012.5
TIME
FIGURE 2
2013
18
HYDROGEN
FLIS -2.70
P/m2.sr.s.MeV
LIS
FLIS
10
12.0
8 MV
10.0
08.0
98-99
PAM 09.7
136 MV
16 MV
1
24 MV
80 MV
HTS=220 MV
1 AU=265 MV
10
100
ENERGY (MeV)
FIGURE 3
1000
19
HELIUM
FLIS -2.70
FLIS
P/m2.sr.s.MeV/nuc
LIS
1
12.0
10.0
08.0
8 MV
136 MV
16 MV
24 MV
98-99 PAM 09.7
80 MV
HTS=220 MV
0.1
1AU=265 MV
10
100
ENERGY (MeV)
FIGURE 4
1000
20
K1, K1H (x 6x1020 cm2.s-1)
10
3
K1
10
2
ELECTRONS
NUCLEI
K1H
10
10
100
1000
RIGIDITY (MV)
FIGURE 5
10000
21
10
H
ln (j2/j1)
He
~P-1.0
1
~P-1.0
GRADIENT
(%/AU)
10
1
0.1
1
P (GV)
FIGURE 6
10
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